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Interval-valued bipolar complex fuzzy soft sets and their applications in decision making.

Abdul Jaleel1, Tahir Mahmood2, Walid Emam3

  • 1Department of Mathematics and, Stats, International Islamic University Islamabad, Islamabad, Pakistan.

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|May 21, 2024
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Summary

This study introduces interval-valued bipolar complex fuzzy soft sets (IVBCFSS), a novel generalization of existing fuzzy set theories. The research explores their operational laws, aggregation operators, and a decision-making method, demonstrating their practical applications.

Keywords:
Aggregation operatorsBipolar complex fuzzy soft setsComplex setDecision-making approachFuzzy setInterval-valued fuzzy soft setSoft sets

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Area of Science:

  • Mathematics
  • Computer Science
  • Fuzzy Set Theory

Background:

  • Fuzzy set theory has evolved through various extensions, including interval-valued, bipolar, complex, and soft sets.
  • Existing theories lack a unified framework to integrate these diverse extensions.
  • There is a need for generalized fuzzy set structures to handle complex decision-making problems.

Purpose of the Study:

  • To introduce and define the interval-valued bipolar complex fuzzy set (IVBCFS) and interval-valued bipolar complex fuzzy soft set (IVBCFSS).
  • To explore the fundamental operational laws, algebraic properties, and aggregation operators for IVBCFSS.
  • To develop and demonstrate a decision-making method based on IVBCFSS to showcase its practical utility.

Main Methods:

  • Formal definition of IVBCFS and IVBCFSS.
  • Investigation of basic operational laws: complement, extended union, extended intersection, restricted union, restricted intersection, AND product, OR product.
  • Development of aggregation operators: IVBCFS average aggregation and IVBCFS geometric aggregation.
  • Formulation of a decision-making algorithm using IVBCFSS.

Main Results:

  • The paper establishes the foundational framework for IVBCFSS, extending existing fuzzy set concepts.
  • Key algebraic operations and aggregation operators for IVBCFSS are defined and their properties analyzed.
  • A novel decision-making method is proposed and illustrated with examples, demonstrating the effectiveness of IVBCFSS.

Conclusions:

  • IVBCFSS provides a powerful and generalized framework for representing and manipulating complex uncertain information.
  • The proposed operational laws and aggregation operators are essential for practical applications of IVBCFSS.
  • The developed decision-making method highlights the superiority and applicability of IVBCFSS in real-world scenarios compared to existing approaches.